The general methodology of "algebraizing" logics is used here for combining different logics. The combination of logics is represented as taking the colimit of the constituent logics in the category of algebraizable logics. The cocompleteness of this category as well as its isomorphism to the corresponding category of certain first-order theories are proved.
"Combining Algebraizable Logics." Notre Dame J. Formal Logic 37 (2) 366 - 380, Spring 1996. https://doi.org/10.1305/ndjfl/1040046092